Line Integral Fundamental Theorem

[killersanta]

Homework Statement

Use Your Phi(from part 1) and the fundamental theorem of line integrals to evaluate the same line integral. (should get the same answer!)

The Attempt at a Solution

Phi from part 1: Phi = xy+ y^2 +C

The line from before go from (0,2) to (-2,0)

r(a) = (0,2) r(b)= (-2,0)

Gradient F * Dr = f(r(b))-f(r(a))
= f(-2,0)-f(0,2)
= (-2*0+0^2)- (0*2+2^2)=4

I'm not sure if this is right, it's not the same answer I got before, I'm not sure what one I got wrong.

 

[snipez90]

For one, you're clearly missing a minus sign.

 

[killersanta]

For one, you're clearly missing a minus sign.

Other than that is it good?